| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2006 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Direct collision, find impulse magnitude |
| Difficulty | Moderate -0.8 This is a straightforward M1 collision problem requiring direct application of conservation of momentum to find one unknown velocity, then calculating impulse using the impulse-momentum theorem. Both are standard textbook procedures with no conceptual challenges or novel problem-solving required. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| (a) CLM: \(0.4 \times 6 - 0.3 \times 2 = 0.4 \times v + 0.3 \times 3 \Rightarrow v = (+) 2.25 \text{ m s}^{-1}\) ('+' ⇒) direction unchanged | M1 A1 A1∇ | (4) |
| (b) \(I = 0.3 \times (2 + 3) = 1.5 \text{ Ns}\) (o.e.) | M1 A1, B1 | (3) |
| (a) CLM: $0.4 \times 6 - 0.3 \times 2 = 0.4 \times v + 0.3 \times 3 \Rightarrow v = (+) 2.25 \text{ m s}^{-1}$ ('+' ⇒) direction unchanged | M1 A1 A1∇ | (4) |
| (b) $I = 0.3 \times (2 + 3) = 1.5 \text{ Ns}$ (o.e.) | M1 A1, B1 | (3) |
**Guidance:**
- (a) M1 for 4 term equation dimensionally correct (± $g$). A1 answer must be positive. A1 f.t. – accept correct answer from correct working without justification; if working is incorrect allow f.t. from a clear diagram with answer consistent with their statement; also allow A1 if their ans is +ve and they say direction unchanged.
- (b) M1 – need (one mass) × (sum or difference of the two speeds associated with the mass chosen). A1 – answer must be positive. B1 allow o.e. e.g. kg m s$^{-1}$
---2. Two particles $A$ and $B$ have mass 0.4 kg and 0.3 kg respectively. They are moving in opposite directions on a smooth horizontal table and collide directly. Immediately before the collision, the speed of $A$ is $6 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and the speed of $B$ is $2 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. As a result of the collision, the direction of motion of $B$ is reversed and its speed immediately after the collision is $3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. Find
\begin{enumerate}[label=(\alph*)]
\item the speed of $A$ immediately after the collision, stating clearly whether the direction of motion of $A$ is changed by the collision,
\item the magnitude of the impulse exerted on $B$ in the collision, stating clearly the units in which your answer is given.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2006 Q2 [7]}}